Question

A random sample of 25 Apple (the company) customers who call Apple Care Support line had an average (X) wait time of 187 seconds with a sample standard deviation (s) of 50 seconds. The goal is to construct a 90% confidence interval for the average (u) wait time of all Apple customers who call for support. Assume that the random variable, wait time of Apple customers (denoted by X), is normally distributed. The standard error (SE) of X is Select one:

a. 2
b. 50
C. 10
d. 37.

The critical value (CV) needed for 90% confidence interval estimation is Select one:

a. 1.28
b. 0.05
c. 1.71
d. 0.1

Answer 1

Standard error: C. 10

Critical value: c. 1.71

Explanation:

Standard error:

`S_(E) = (s)/(√(n))`

In which s is the standard deviation of the sample and n is the size of the sample.

In this problem,
`s = 50, n = 25`

So

`S_(E) = (50)/(√(25)) = 10`

Which means that the answer for the first question is c.

Critical value

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95. So we have T = 1.71, which means that the answer for the second question is also c.